Question: For integers $a$, $b$, and $k$, we know that $a>12$, $b<20$, and $a<b$. If $b=7k$, what is the value of $k$?
Answer: The equation $b=7k$ implies that $b$ is a multiple of $7$. Since $12<a<b<20$, $b$ is a multiple of 7 between 12 and 20. This implies $b=14$, so $k=\boxed{2}$.